By means of a surface-integral formalism we derive the integral equations for diffuse photon density waves with boundary conditions corresponding to a diffuse–diffuse interface with index mismatch and solve them numerically without any approximation. These numerical results are verified with Monte Carlo simulations for the planar interface case. Since the application of the boundary condition to index-mismatched media is difficult, an approximation that yields very accurate values is found. This approximation can be easily introduced into analytical models, and a study of its limit of validity is shown. We demonstrate with numerical results that the multiple-scattering contribution that is due to surface roughness can be neglected, even when index mismatch is present.

© 1999 Optical Society of America

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